$A$ $B$ $C$ If: $ AB = 4x + 6$, $ AC = 22$, and $ BC = 7x + 5$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 6} + {7x + 5} = {22}$ Combine like terms: $ 11x + 11 = {22}$ Subtract $11$ from both sides: $ 11x = 11$ Divide both sides by $11$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 7({1}) + 5$ Simplify: $ {BC = 7 + 5}$ Simplify to find ${BC}$ : $ {BC = 12}$